Triangle overview

The trigonometric functions describes relations among angles in a triangle. See the following image:

The triangle <i>ABC</i>

We see the triangle consisting of three vertices A, B and C. We commonly refer to such triangle as triangle ABC or △ABC. Each pair of vertices forms a side in the triangle. We have three sides in the triangle: AB, BC and AC. As you can see the side AB has an alternative name “c”. This name is derived from the only vertex that is not part of the side. So the side BC has an alternative name “a” since the vertex A is not part of the side BC. We use small letters for such alternative names.

Each triangle has three inner angles. By convention we use Greek letters α (alpha), β (beta) and γ (gamma) to mark these angles. The angle α is next to the vertex A etc. See the following picture.

Triangle <i>ABC</i> with marked angles

We can use trigonometric functions in any triangle but often we use trigonometric metric functions in right-angeled triangles. A right-angeled triangle is a triangle in which one angle is a right angle. Right angle means 90-degree angle. See the example:

The right-angeled triangle <i>ABC</i>

In the right-angeled triangle each side has it’s own name. The longest one is called hypotenuse. The hypotenuse is always on the opposite side than the right angle. The other twe sides are called legs. The two legs always forms the right angle and are always shorter than the hypotenuse.